Thank you for being so willing to take pics and videos, and answering questions!
It does help a lot.
I'm afraid I can't help much with the one that was on it's side, that's really worrying. But it sounds as though it improved after the water change, so I would personally do daily 50% water changes for a while. Don't clean the filter unless the flow slows or it seems blocked - let the new media get properly colonised, then make sure to only rinse the media out in old tank water once you do begin cleaning it in a few weeks time.
How long have you had these guys? My impression of your tank is that it's very pretty and clean, I can see how much work and effort you've put into it! So the following isn't a criticism at all, just some optional suggestions based on my experience with cories.
The sand is very pale, which can make fish look washed out and pale. It's not typical for their wild environment, you know? They're used to a darker substrate. The tank is also very open and exposed - and so importantly for wild caught fish especially, cories like to have spots they can hide in. In the vid the cory spooked, but had nowhere to hide, so sat and panted, looking stressed. Stress kills fish, and it would be a good start to add a good amount of hardscape and planting/leaves that would help them feel safer and more secure. Let them hide away when scared or sleeping, and they'll be less stressed.
So I would add a load of Indian almond leaves, to help provide some cover over the substrate, and for the beneficial properties they have. Oak and Beech leaves are also good alternatives. I'd add a lot of "furniture" to provide hiding spots. Like pieces of driftwood and/or stone, coconut huts, or terracotta pots, whatever you can add that will give them little corners and areas to hide away in. Some dense planting can help too, some bunches of java fern weighted and left to sit on the substrate or attached to decor low down works, or bunches of crytocorynes planted to provide a hidy corner.
I truly believe this will help your fish out a lot.